In an optically amplified transmission system employing non-coherent detection the optical transmission path between an optical transmitter and a receiver at some remote location includes a concatenation of optical amplifiers distributed at spaced intervals along that transmission path. Each of the optical amplifiers has a gain medium which has a population inversion. A low power input to such an amplifier is amplified to a higher power as it propagates through the gain medium. The signal input to the amplifier interacts with the population inversion to produce stimulated emission, thereby resulting in signal amplification. Additionally however, the population inversion will produce some spontaneous emission which is broad-band in comparison with the signal, and this spontaneous emission will also be amplified both in this, and in succeeding amplifiers. As a result, amplified spontaneous emission (ASE) arrives at the receiver together with the signal. It has been shown, for instance in a paper by N. A. Olsson entitled `Lightwave Systems with Optical Amplifiers`, Journal of Lightwave Technology, Vol. 7, No. 7, Jul. 1989, pp 1071-1082, that when the incoming signal is detected at the receiver, the ASE contributes a noise input as the result of signal-spontaneous beat interactions and a further noise input as the result of spontaneous-spontaneous beat interactions.